Pangloss

The name Pangloss was created through use of Greek Prefix
pan meaning all, or every, and ... from the Greek root,
gloss meaning tongue, language and speech, making "Pangloss"
mean ... "all talk".
- Wikipedia, "Pangloss" 2-18-2008

Parallelism

Pangloss attempts to decrease running times for problems by introducing parallelism at the data and task levels. To be specific, we cannot claim to increase
speed by data parallelism and task parallelism in general, but only for problems that do not have heavy dependencies in the data and for problems that can
be explicitly separated into task, respectively.

Our machine is a shared memory MIMD (Multiple Instruction Multiple Data) cluster. Pangloss uses NFS to allow compute nodes to access the data used in a
computation; this feature was largely inspired by Microwulf.
Now is probably a good time to announce that Pangloss is merely a customization of Microwulf. We
have added, and left out, many of the core features of Microwulf, to serve our particular interests. It is not difficult to see the aesthetic similarities between
the two machines. Also, it should be made clear, that we have no affiliation with Microwulf; we merely admire the team's work.

Amdahl's Rules Of Thumb

Combining Amdahl's balanced system law and his memory law, we can see that 1 byte of memory and 1 bit per second of I/O are required for each instruction
per second supported by a computer (Wikipedia - Amdahl's Law). This rule also goes by the title Amdahl's Other Law.

Pangloss's Rules Of Thumb

We agree that Amdahl's Law appears accurate in the theoretical universe. However, in one model of the universe, how would one account for the heavy,
GUI-ridden, modern operating systems that must remain in memory and the cache. Of course, Amdahl may have factored in this thought or operating systems of his time may have
been lighter. Our team is in no position to make any claims about this or the correctness of his rule. However, in the case that this alluded Amdahl,
we have increased the processing power and RAM on each of our compute nodes by a factor of 1.5x. Our thinking is that this extra speed and space will
not only account for the operating system's footprint, but will also give extra room for caching and paging, and hence will allow for a significant speed up
in measured flops.

Physics

Airflow

When attempting to pack many motherboards and processors into one box, one must take careful note of proper airflow to cool the system. For Pangloss, we
used only motherboards with built in GbE interfaces. Without cards orthogonal to the motherboard (with the exception of the RAM chips), turbulance
is minimized and airflow is streamlined across the boards and CPUs. This also allows us to stack motherboards closer together, saving vertical space in the
hardware case.

Cable Runs

We have kept Pangloss's cable runs short and uniform, for each compute node. This ensures a minimum physical distance data is sent over.

Problem

Pangloss is intended to be a test bed for students, to learn about parallel problem solving. Early on, we decided to work on a problem that is:

Easy for the layman to understand;

Interesting and exciting, for a Computer Science student;

Easily parallizable;

Leibniz's Formula for π

It has been said that Gottfried Leibniz was greatly interested in the metaphysical aspects of numbers. In one of his metaphysical excursions, Leibniz
discovered that there was an infinite series that would sum to π. In the time of Leibniz, it would have been unreasonable to calculate the sum of
a finite series that closely approximated π.

From Leibniz's time to the current day, there have been many improvements in methods for approximating π. As of February 2008, π has been calculated to
over 1012 digits. It would take an impractical number of terms of the Leibniz series to calculate π to this accuracy. For this reason, Leibniz's Formula for
π has not seen much light. In this project, we hope to use Leibniz's Formula to calculate more correct sequential digits of π, than have already been calculated
using Leibniz's Formula. We do realize that there are more efficient ways to calculate π, however, we have choosen this method for metaphysical reasons.

To calculate π, Pangloss will use the formula:

Equation 1: Leibniz's Formula for π

Team

Richard Faulkner

Garrett Richard

Ojasvi Dubey

Rubab Sayeed

Evan O'Donovan

Kent Klymenko

Cameron McInally

Conclusions

In general, our project has failed. One of our motherboards was D.O.A. and another had faulty fans which was worrisome. We were able to get 3 nodes fully functional and running. A complete hardware manifest can be found here. With the set backs we have encountered, we have not attempted to compute the Leibniz Series.